Vol. 29, No. 3, 1969

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Infinite semigroups whose non-trivial homomorphs are all isomorphic

Bruce Ansgar Jensen

Vol. 29 (1969), No. 3, 583–591

An infinite semigroup S such that every nontrivial homomorph of it is isomorphic to S is called an HI semigroup. Every commutative HI semigroup is a group and thus it is isomorphic to the group Z(p), for some prime P. An infinite Brandt semigroup is HI if and only if it has a trivial structure group. An inverse HI semigroup containing a primitive idempotent is either Brandt or else it is isomorphic to a trasfinite chain of extensions of a Brandt semigroup K by isomorphic copies of K (where K has the trivial group as its structure group). Necessary and sufficient conditions are given for a semigroup of the latter type to yield an HI semigroup and an example is constructed.

Mathematical Subject Classification
Primary: 20.93
Received: 25 October 1967
Published: 1 June 1969
Bruce Ansgar Jensen